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MR901625 (88g:58171) 58G10 (58G11)
Bismut, Jean-Michel; Cheeger, Jeff Invariants êta et indice des familles pour des variétés à bord. (French) [Eta invariants and the families' index for manifolds with boundary] C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 4, 127–130.
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